4-dimensional Variational Data Assimilation Research Articles

European pollen reanalysis, 1980–2022, for alder, birch, and olive

The dataset presents a 43 year-long reanalysis of pollen seasons for three major allergenic genera of trees in Europe: alder (Alnus), birch (Betula), and olive (Olea). Driven by the meteorological reanalysis ERA5, the atmospheric composition model SILAM predicted the flowering period and calculated the Europe-wide dispersion pattern of pollen for the years 1980–2022. The model applied an extended 4-dimensional variational data assimilation of in-situ observations of aerobiological networks in 34 European countries to reproduce the inter-annual variability and trends of pollen production and distribution. The control variable of the assimilation procedure was the total pollen release during each flowering season, implemented as an annual correction factor to the mean pollen production. The dataset was designed as an input to studies on climate-induced and anthropogenically driven changes in the European vegetation, biodiversity monitoring, bioaerosol modelling and assessment, as well as, in combination with intra-seasonal observations, for health-related applications.

Assessing the impact of subsurface temperature observations from fishing vessels on temperature and heat content estimates in shelf seas: a New Zealand case study using Observing System Simulation Experiments

We know that extremes in ocean temperature often extend below the surface, and when these extremes occur in shelf seas they can significantly impact ecosystems and fisheries. However, a key knowledge gap exists around the accuracy of model estimates of the ocean’s subsurface structure, particularly in continental shelf regions with complex circulation dynamics. It is well known that subsurface observations are crucial for the correct representation of the ocean’s subsurface structure in reanalyses and forecasts. While Argo floats sample the deep waters, subsurface observations of shelf seas are typically very sparse in time and space. A recent initiative to instrument fishing vessels and their equipment with temperature sensors has resulted in a step-change in the availability of in situ data in New Zealand’s shelf seas. In this study we use Observing System Simulation Experiments to quantify the impact of the recently implemented novel observing platform on the representation of temperature and ocean heat content around New Zealand. Using a Regional Ocean Modelling System configuration of the region with 4-Dimensional Variational Data Assimilation, we perform a series of data assimilating experiments to demonstrate the influence of subsurface temperature observations at two different densities and of different data assimilation configurations. The experiment period covers the 3 months during the onset of the 2017-2018 Tasman Sea Marine Heatwave. We show that assimilation of subsurface temperature observations in concert with surface observations results in improvements of 44% and 38% for bottom temperature and heat content in shelf regions (water depths< 400m), compared to improvements of 20% and 28% for surface-only observations. The improvement in ocean heat content estimates is sensitive to the choices of prior observation and background error covariances, highlighting the importance of the careful development of the assimilation system to optimize the way in which the observations inform the numerical model estimates.

Comparison of 4-dimensional variational and ensemble optimal interpolation data assimilation systems using a Regional Ocean Modeling System (v3.4) configuration of the eddy-dominated East Australian Current system

Abstract. Ocean models must be regularly updated through the assimilation of observations (data assimilation) in order to correctly represent the timing and locations of eddies. Since initial conditions play an important role in the quality of short-term ocean forecasts, an effective data assimilation scheme to produce accurate state estimates is key to improving prediction. Western boundary current regions, such as the East Australia Current system, are highly variable regions, making them particularly challenging to model and predict. This study assesses the performance of two ocean data assimilation systems in the East Australian Current system over a 2-year period. We compare the time-dependent 4-dimensional variational (4D-Var) data assimilation system with the more computationally efficient, time-independent ensemble optimal interpolation (EnOI) system, across a common modelling and observational framework. Both systems assimilate the same observations: satellite-derived sea surface height, sea surface temperature, vertical profiles of temperature and salinity (from Argo floats), and temperature profiles from expendable bathythermographs. We analyse both systems' performance against independent data that are withheld, allowing a thorough analysis of system performance. The 4D-Var system is 25 times more expensive but outperforms the EnOI system against both assimilated and independent observations at the surface and subsurface. For forecast horizons of 5 d, root-mean-squared forecast errors are 20 %–60 % higher for the EnOI system compared to the 4D-Var system. The 4D-Var system, which assimilates observations over 5 d windows, provides a smoother transition from the end of the forecast to the subsequent analysis field. The EnOI system displays elevated low-frequency (>1 d) surface-intensified variability in temperature and elevated kinetic energy at length scales less than 100 km at the beginning of the forecast windows. The 4D-Var system displays elevated energy in the near-inertial range throughout the water column, with the wavenumber kinetic energy spectra remaining unchanged upon assimilation. Overall, this comparison shows quantitatively that the 4D-Var system results in improved predictability as the analysis provides a smoother and more dynamically balanced fit between the observations and the model's time-evolving flow. This advocates the use of advanced, time-dependent data assimilation methods, particularly for highly variable oceanic regions, and motivates future work into further improving data assimilation schemes.

Weak constraint 4D-Var data assimilation in the Regional Ocean Modeling System (ROMS) using a saddle-point algorithm: Application to the California Current Circulation

The saddle-point formulation of weak constraint 4-dimensional variational (4D-Var) data assimilation has been developed for the Regional Ocean Modeling System (ROMS), and is applied here to the California Current System (CCS). Unlike the conventional primal and dual forcing formulation of weak constraint 4D-Var, the saddle-point formulation can be efficiently parallelized in time, leading to a substantial decrease in wall-clock run time. The performance of the ROMS saddle-point 4D-Var algorithm is assessed here and compared to that of the dual forcing formulation which is the current standard in ROMS. While the rate of convergence of the saddle-point formulation is slower than the dual forcing formulation, the increase in computational speed due to time-parallelization can more than compensate for the additional inner-loop iterations required by the saddle-point algorithm in the CCS configuration considered here. Further gains in performance can be achieved by running the 4D-Var inner-loop iterations at reduced resolution and/or reduced arithmetic precision. The results presented here indicate that in high performance computing environments with large numbers of available compute cores, the saddle-point formulation of 4D-Var could significantly reduce the run-time compared to the dual forcing formulation for large data assimilation problems.

4D-Var data assimilation in a nested model of the Mid-Atlantic Bight

The Regional Ocean Modeling System (ROMS) 4-dimensional variational (4D-Var) data assimilation platform has been extended to include nested grid configurations using both one-way and two-way nesting strategies. The efficacy of this new ROMS utility is demonstrated in a model comprising three nested grids with horizontal refinement and configured for the Mid-Atlantic Bight. The three nested grids have a horizontal resolution ranging from ∼7 km to ∼0.8 km thereby capturing circulation regimes that span the Gulf Stream western boundary current, through the mesoscale eddy field, and down to the rapidly evolving and energetic submesoscale. These circulation regimes represent a challenge for any data assimilation system, and the nested 4D-Var system was found to perform well across the range of resolved space and time scales. The observational data used to constrain the ocean state estimates come from a wide range of remote sensing, in situ, and mobile platforms, along with the U.S. National Science Foundation’s Ocean Observatories Initiative Pioneer Array. Several aspects of the system performance are explored and described here, including the fit of the model to the observations, the influence of data assimilation on the wave number spectra at the submesoscale, and the downscaling and upscaling of information captured by the observations.

Forecast Sensitivity-based Observation Impact (FSOI) in an analysis–forecast system of the California Current Circulation

Forecast Sensitivity-based Observation Impacts (FSOI) in an analysis–forecast​ system of the California Current System (CCS) are quantified using an adjoint-based approach. The analysis–forecast system is based on the Regional Ocean Modeling System (ROMS) and a 4-dimensional variational (4D-Var) data assimilation approach. FSOI was applied to four different metrics of forecast skill that target important features of the CCS circulation along the central California coast. A particular focus of the FSOI analysis is the impact of assimilation of measurements of the radial component of surface currents from a network of high frequency (HF) radars since this is a new data stream in the near-real-time system considered here. On average, ∼50–60% of all observations assimilated into the model yielded improvements in the forecast skill. Conversely, the remaining ∼40–50% of data degrade the forecasts, in line with similar findings in numerical weather prediction systems. Much of the improvement in forecast skill arises from remotely sensed observations, including HF radar data; on average only ∼50% of in situ measurements contribute to a reduction in forecast error. This is partly due to the large volume of remote sensing observations compared to in situ observations. However, in situ observations are an order of magnitude more impactful than remotely sensed data when viewed in terms of the average impact per observation.

The sensitivity of the WRF-4DVar data assimilation system to the control variables: A study on heavy rainfall events over India

The impact of different formulations of background error covariances (BECs) is examined for three heavy rainfall episodes over north India with a regional 4-dimensional variational (4DVar) data assimilation (DA) system. Three BEC formulations are analyzed, in which two of them employ stream function and velocity potential (ψ and χ) and the third one uses zonal and meridional velocity components (v and v) as momentum control variables. The uv-based formulation is completely univariate whereas, the correlations among the control variables are taken into account in the ψχ-based formulations through linear regression relations. Among the two ψχ-based BECs, one uses univariate relation and the other one uses multivariate relations for the moisture field. The multivariate relationship allows for impacting the moisture analysis through the assimilation of temperature or wind observations. Three experiments are carried out for each case with cyclic 4DVar assimilation. The conventional surface and upper-air observations are assimilated in combination with atmospheric motion vectors (AMVs) and ocean surface winds. Free forecast for 48 h is performed from respective final analysis fields for all the experiments. The results indicate that the uv-based analysis fields are closer to the observations. A comparative analysis of the 4DVar experiments with the 3DVar DA system provided a critical insight on the role of the 4DVar DA system on implicitly accounting for the multivariate correlations. The precipitation forecasts confirm the improved performance of the ψχ-based experiment, when multivariate nature of the humidity is incorporated. The time evolution of the intense rainfall episodes over the location of maximum rainfall are relatively well reproduced in the uv-based experiment. The results indicate that the inclusion of multivariate humidity variable in the BEC formulation does have a significant impact on suppressing the excessive overestimation in rainfall intensity.

The impact of ocean data assimilation on the simulation of mesoscale eddies at São Paulo plateau (Brazil) using the regional ocean modeling system

This work presents simulations of ocean circulation in the southwestern South Atlantic Ocean with emphasis on the São Paulo Plateau region, a unique physiographic feature at the foot of the continental slope offshore southeast Brazil, where the flow is dominated by ocean eddies and dipoles. Surface dynamics south of 23°S presents a heterogeneous circulation pattern intimately related to the presence of mesoscale features, such as meanders of the Brazil Current along the continental slope, and eddies that interacts with deep ocean features. The reproduction of these eddies at the correct time and spatial structure are quite challenging in the context of a non-assimilative model, considering the limitations imposed by the model’s numerical schemes, physical parameterizations, boundary conditions and surface forcing. In this sense, the Regional Ocean Modeling System (ROMS) 4-dimensional Variational Data Assimilation (4D-Var) module was used to increase model skill and minimize deviations from oceanic observations. Weekly observations of Sea Surface Height (SSH), daily Sea Surface Temperature (SST) fields and in situ vertical profiles of temperature and salinity from multiple sources were used in consecutive assimilation cycles to produce an accurate representation of ocean features and their variability. Both the assimilative and free run were evaluated against observations, including in situ current measurements. Results showed significant improvements of the assimilation procedure on both assimilated and non-assimilated variables, with RMSE reductions of 27% and 47% for SST and SSH, respectively, and 51% for current speed measurements during a dipole event in the São Paulo Plateau. The assimilative run was able to reproduce a remarkable event of mesoscale eddies interaction (dipole) and consequent current intensification, leading to important improvements on model skill. The correct use of observational information of open ocean surface features through data assimilation is a key factor for a proper simulation of such eddy dipole events.

Assessing the performance of an ocean observing, analysis and forecast System for the Mid-Atlantic Bight using array modes

The efficacy of an ocean observing, analysis, and forecasting system for the Mid-Atlantic Bight and the Gulf of Maine is explored using the concept of array modes. The analysis-forecast system is based on a triply nested configuration of the Regional Ocean Modeling System (ROMS) in conjunction with 4-dimensional variational (4D-Var) data assimilation. The array modes identify the degrees of freedom (df) of the signal and of the noise resolved by the observations, and are used here to quantify the extent to which the existing network of platforms and instruments are able to observe the ocean across different dynamical regimes ranging from quasi-geostrophic through the mesoscale and down to the sub-mesoscale. The ocean observing system includes the U.S. National Science Foundation’s Ocean Observatories Initiative Pioneer Array. In general, it is found that the df of the signal are largely associated with in situ observations from the Pioneer Array. On the other hand, a combination of satellite remote sensing and in situ observations potentially contribute to the df of the noise associated with uncertainties in the measurements. The array modes also provide information about the reduction in the expected analysis and forecast error covariance due to assimilating the observations. Here too observations from the Pioneer Array are found to significantly influence the veracity of the analyses and forecasts, and the circulation is instrumental in propagating observational information to other parts of the model domain. An approach is presented in which the array modes are used to quantify the impact of data assimilation on the expected forecast error covariance of forecasts initialized from the 4D-Var ocean state estimates. The advantage of this approach over others in common use is that it is independent of forecast error norm and circumvents the need for generating potentially large and costly ensembles.

Inverse modelling of carbonyl sulfide: implementation, evaluation and implications for the global budget

Abstract. Carbonyl sulfide (COS) has the potential to be used as a climate diagnostic due to its close coupling to the biospheric uptake of CO2 and its role in the formation of stratospheric aerosol. The current understanding of the COS budget, however, lacks COS sources, which have previously been allocated to the tropical ocean. This paper presents a first attempt at global inverse modelling of COS within the 4-dimensional variational data-assimilation system of the TM5 chemistry transport model (TM5-4DVAR) and a comparison of the results with various COS observations. We focus on the global COS budget, including COS production from its precursors carbon disulfide (CS2) and dimethyl sulfide (DMS). To this end, we implemented COS uptake by soil and vegetation from an updated biosphere model (Simple Biosphere Model – SiB4). In the calculation of these fluxes, a fixed atmospheric mole fraction of 500 pmol mol−1 was assumed. We also used new inventories for anthropogenic and biomass burning emissions. The model framework is capable of closing the COS budget by optimizing for missing emissions using NOAA observations in the period 2000–2012. The addition of 432 Gg a−1 (as S equivalents) of COS is required to obtain a good fit with NOAA observations. This missing source shows few year-to-year variations but considerable seasonal variations. We found that the missing sources are likely located in the tropical regions, and an overestimated biospheric sink in the tropics cannot be ruled out due to missing observations in the tropical continental boundary layer. Moreover, high latitudes in the Northern Hemisphere require extra COS uptake or reduced emissions. HIPPO (HIAPER Pole-to-Pole Observations) aircraft observations, NOAA airborne profiles from an ongoing monitoring programme and several satellite data sources are used to evaluate the optimized model results. This evaluation indicates that COS mole fractions in the free troposphere remain underestimated after optimization. Assimilation of HIPPO observations slightly improves this model bias, which implies that additional observations are urgently required to constrain sources and sinks of COS. We finally find that the biosphere flux dependency on the surface COS mole fraction (which was not accounted for in this study) may substantially lower the fluxes of the SiB4 biosphere model over strong-uptake regions. Using COS mole fractions from our inversion, the prior biosphere flux reduces from 1053 to 851 Gg a−1, which is closer to 738 Gg a−1 as was found by Berry et al. (2013). In planned further studies we will implement this biosphere dependency and additionally assimilate satellite data with the aim of better separating the role of the oceans and the biosphere in the global COS budget.

On the behavior of ocean analysis and forecast error covariance in the presence of baroclinic instability

The properties of the expected analysis and forecast error covariance matrices are explored using a novel method based on the tangent linearization and adjoint of a 4-dimensional variational (4D-Var) data assimilation system. The method is applied to the mesoscale circulation that develops in the presence of a baroclinically unstable mid-latitude ocean temperature front using a series of paternal twin experiments that employ both strong and weak constraint 4D-Var. Adopting the traditional view of Empirical Orthogonal Functions (EOFs) of a covariance matrix as the semi-major axes of a multi-dimensional hyper-ellipsoid, variations in the volume of the analysis and forecast error hyper-ellipsoids are explored which provides information about the flow of probability through state–space. The complementary variations in the expected total variance of the covariance matrix are also investigated. Two different kinds of behavior are identified that are associated with either the demise or growth of baroclinic instabilities. In both cases, the volume of the hyper-ellipsoid decreases during the 4D-Var analysis cycle. During the subsequent forecasts, the volume of the forecast error hyper-ellipsoid initially continues to collapse under both scenarios. During this time, the hyper-ellipsoid becomes increasingly elongated along some of the semi-major axes as forecast errors grow in preferential directions. Growth in these directions is controlled by the most unstable error modes, and projection of forecast error on to the precursors of these modes has been shown previously to be characterized by upscale energy transfer and non-normal processes. For the case of the growing wave, the forecast error hyper-ellipsoid continues to collapse through to the end of the forecast period. However, for the decaying wave, the hyper-ellipsoid may undergo expansion at longer forecast lead times.

Observation impacts on the Mid-Atlantic Bight front and cross-shelf transport in 4D-Var ocean state estimates: Part II — The Pioneer Array

The Regional Ocean Modeling System (ROMS) 4-dimensional variational (4D-Var) data assimilation system was used to compute ocean state estimates of the Mid-Atlantic Bight (MAB). A three-level nested grid configuration was employed with horizontal resolution successively enhanced from 7 km down to 800 m at the innermost nest. This captures the dynamics on space- and time-scales ranging from the Gulf Stream western boundary current down to the rapidly evolving and energetic sub-mesoscale circulation. This is a companion study to Levin et al. (2020) which examined the overall impacts of the entire observing system on shelf-break exchange. This follow-on study specifically focuseson the impact of the in situ elements of the ocean observing system on the 4D-Var analyses. The particular focus here is on the Pioneer Array, a high-density observing system in the MAB designed to measure the multi-scale nature of shelf-break exchange processes. Building on Levin et al. (2020), it is found that the relative impact of observations from different components of the Pioneer Array depends on the scales of motion that are resolved by each nested grid. This is in apparent agreement with the linear theory of geostrophic adjustment despite the O(1) Rossby number. The synergy between the observations from different observing platforms has also been quantified by comparing the observation impacts with the sensitivity of the 4D-Var analyses to changes in the observing array. It is found that while some observations do not have a significant direct impact on the analyses, they nevertheless provide essential information about the presence of circulation features, corroborating that measured by other sensors. Thus, the individual parts of the observing system can borrow strength from each other. Finally, the contribution of each component of the observing system to the expected error in the 4D-Var analyses was also quantified, where the critical role played by the Pioneer Array moorings in resolving the sub-mesoscale circulation is again highlighted.

Observation impacts on the Mid-Atlantic Bight front and cross-shelf transport in 4D-Var ocean state estimates: Part I — Multiplatform analysis

A nested configuration of the Regional Ocean Modeling System (ROMS) comprising three grids was used in conjunction with a 4-dimensional variational (4D-Var) data assimilation system to compute ocean state estimates of the Mid-Atlantic Bight (MAB). The three nested grids have a horizontal resolution ranging from ∼7 km to ∼0.8 km and capture circulation regimes that span the Gulf Stream western boundary current, through the mesoscale eddy field, and down to the rapidly evolving and energetic sub-mesoscale. All of these circulation regimes are challenging for any data assimilation system, yet the 4D-Var system was found to perform well across this range of space- and time-scales. The observational data used to constrain the ocean state estimates comes from a wide range of remote sensing, in situ, and mobile platforms. An adjoint-based procedure was used to compute the impact of each observing platform on several different indexes that describe the position of the MAB front, stratification, and associated cross-shelf exchange processes in the vicinity of the U.S. National Science Foundation’s Ocean Observatories Initiative Pioneer Array. The impact of observations from each observing platform on the chosen indexes varies across the three grids. It is a function of several factors that include the nature of the background circulation and the level of error assumed for the background ocean state and the observations. The geographic distribution of the observation impacts is remarkably robust across the various indexes and the three grids. In addition, observations that are both local to and remote from the target regions that define each index can exert a significant influence on the circulation. Variations in the observation impacts through time can be used to identify observations that exert unexpectedly large influence on the 4D-Var analyses (i.e, outliers), and routine monitoring of observation impacts is a useful indicator of the efficacy of different components of the observing system. Also, the observation impacts were found to be a useful performance indicator for the data assimilation system.

Ensemble of 4DVARs (En4DVar) data assimilation in a coastal ocean circulation model, Part I: Methodology and ensemble statistics

The ocean state off Oregon-Washington, U.S. West coast, is highly variable in time. Under these conditions the assumption made in traditional 4-dimensional variational data assimilation (4DVAR) that the prior model (background) error covariance is the same in every data assimilation (DA) window can be limiting. A DA system based on an ensemble of 4DVARs (En4DVar) has been developed in which the background error covariance is estimated from an ensemble of model runs and is thus time-varying. This part describes details of the En4DVar method and ensemble statistics verification tests. The control run and 39 ensemble members are forced by perturbed wind fields and corrected by DA in a series of 3-day windows. Wind perturbations are represented as a linear combination of empirical orthogonal functions (EOFs) for the larger scales and Daubechies wavelets for the smaller scales. The variance of the EOF expansion coefficients is based on estimates of the wind field error statistics derived using scatterometer observations and a Bayesian Hierarchical Model. It is found that the variance of the wind errors relative to the natural wind variability increases as the horizontal spatial scales decrease. DA corrections to the control run and ensemble members are calculated in parallel by the newly developed, cost-effective cluster search minimization method. For a realistic coastal ocean application, this method can generate a 30% wall time reduction compared to the restricted B-conjugate gradient (RBCG) method. Ensemble statistics are generally found to be consistent with background error statistics. In particular, ensemble spread is maintained without inflating. However, sea-surface height background errors cannot be fully reproduced by the ensemble perturbations.

The impact of remote sensing observations on cross-shelf transport estimates from 4D-Var analyses of the Mid-Atlantic Bight

This paper explores the impact of the individual components of a coastal ocean observing system on estimates of the circulation derived from a state-of-the-art analysis and forecast system for the Mid-Atlantic Bight and Gulf of Maine. The foundation of these activities is the Regional Ocean Modeling System 4-dimensional variational (4D-Var) data assimilation platform, which is run in support of the Mid-Atlantic Regional Association Coastal Ocean Observing System as part of the U.S. Integrated Ocean Observing System. The specific focus of this study is on the impact of remote sensing observations from both space- and land-based platforms on estimates of cross-shelf transport in the vicinity of the National Science Foundation Ocean Observatories Initiative Pioneer array. Sea surface temperature (SST) and sea surface height (SSH) were found to have, on average, a similar impact on the transport estimates. However, during a typical 3-day 4D-Var assimilation cycle, approximately two orders of magnitude more observations of SST than SSH are used in the model, and closer analysis shows that each altimeter measurement has approximately 50 times more impact on the transport estimates than an individual SST observation. This highlights the value of altimetry data for ocean state estimation, and the significance of expanding the altimeter constellation. The observations that are most impactful of all are in situ measurements of temperature and salinity, which have typically 3–4 times more impact than an individual SSH datum. A robust geographical distribution of the observation impacts emerges across a range of transport metrics which results from the combined influence of space-time dynamical interpolation and error covariance information within the 4D-Var system. The observation impact calculations suggest that High Frequency (HF) radar estimates of surface currents have relatively little direct influence on cross-shelf transport estimates. However, quantification of the sensitivity of these same estimates to changes in the observing system indicate that HF radar observations indirectly provide important information. This is understood in the current system by appealing to the idea of borrowing strength from the field of statistics in which some observations (satellite remote sensing in the case considered here) can borrow strength from other, seemingly less important observations.

Mean circulation of the Mid-Atlantic Bight from a climatological data assimilative model

The along-shelf momentum balance of the Mid-Atlantic Bight (MAB) coastal ocean includes a significant contribution from the along-shelf gradient in sea level. This sea level tilt, of order 10−7, and other features of the mean sea level are not captured well in global mean dynamic topography (MDT) derived from hydrographic observations or satellite altimetry and gravity data, and is poorly represented in global and basin scale dynamical models. This is problematic for applications that would use coastal satellite altimeter data to estimate total water level above datum. We have produced a MDT for the MAB using the Regional Ocean Modeling System (ROMS) with 4-dimensional variational (4D-Var) data assimilation configured to obtain climatological annual and monthly mean results. The observations assimilated were a regional hydrographic climatology of temperature and salinity, and long-term mean velocity from HF-radar, shipboard ADCP, and current-meters. Assimilation adjusts the 3-dimensional ocean state, boundary conditions, and air-sea fluxes to minimize the model-data misfit. The assimilation of mean velocity data is vital to obtaining a realistic circulation result. The MDT exhibits a strong across-shelf sea level slope in geostrophic balance with the southwestward mean flow. The subtle along-shelf tilt is recovered and is relatively uniform throughout the MAB inside the 50 m isobath, but on the southern outer shelf it reverses sign and drives significant across-isobath flow, partially draining the southward mean transport. In the north, across-shelf flow is offshore in the surface and bottom Ekman layers, but largely balanced locally by inflow in the interior depth range.

4DVAR Data Assimilation with the Regional Ocean Modeling System (ROMS): Impact on the Water Mass Distributions in the Yellow Sea

In this study, we evaluate the performance of the recently developed incremental strong constraint 4-dimensional variational (4DVAR) data assimilation applied to the Yellow Sea (YS) using the Regional Ocean Modeling System (ROMS). Two assimilation experiments are compared: assimilating remote-sensed sea surface temperature (SST) and both the SST and in-situ profiles measured by shipboard CTD casts into a regional ocean modeling from January to December of 2011. By comparing the two assimilation experiments against a free-run without data assimilation, we investigate how the assimilation affects the hydrographic structures in the YS. Results indicate that the SST assimilation notably improves the model behavior at the surface when compared to the non-assimilative free-run. The SST assimilation also has an impact on the subsurface water structure in the eastern YS; however, the improvement is seasonally dependent, that is, the correction becomes more effective in winter than in summer. This is due to a strong stratification in summer that prevents the assimilation of SST from affecting the subsurface temperature. A significant improvement to the subsurface temperature is made when the in-situ profiles of temperature and salinity are assimilated, forming a tongue-shaped YS bottom cold water from the YS toward the southwestern seas of Jeju Island.

A resonant response of the California Current circulation to forcing by low frequency climate variability

Low frequency variability of the California Current System (CCS) is investigated using circulation estimates based on a 31-year (1980–2010) sequence of historical analyses of the CCS calculated using the Regional Ocean Modeling System (ROMS) 4-dimensional variational (4D-Var) data assimilation system. The leading 3-dimensional multivariate empirical orthogonal functions (3D EOFs) of the CCS circulation were computed and provide a detailed view of low-frequency circulation variability within the CCS. The 3D EOFs are used as basis functions for a linear inverse model of the circulation, and several Principal Oscillation Patterns (POPs) of the circulation are identified. The leading POPs have periods in the range ∼4−10 years, and shed light on the 3-dimensional time evolving structure associated with low-frequency variability in the circulation. A particular focus here is coastal upwelling. In particular, a POP with a period close to 10 years appears to be preferentially excited as a resonant response to forcing associated with the regional expression of the Pacific Decadal Oscillation, the North Pacific Gyre Oscillation and the El Niño Southern Oscillation.

The impact of the ocean observing system on estimates of the California current circulation spanning three decades

Data assimilation is now used routinely in oceanography on both regional and global scales for computing ocean circulation estimates and for making ocean forecasts. Regional ocean observing systems are also expanding rapidly, and observations from a wide array of different platforms and sensor types are now available. Evaluation of the impact of the observing system on ocean circulation estimates (and forecasts) is therefore of considerable interest to the oceanographic community. In this paper, we quantify the impact of different observing platforms on estimates of the California Current System (CCS) spanning a three decade period (1980–2010). Specifically, we focus attention on several dynamically related aspects of the circulation (coastal upwelling, the transport of the California Current and the California Undercurrent, thermocline depth and eddy kinetic energy) which in many ways describe defining characteristics of the CCS. The circulation estimates were computed using a 4-dimensional variational (4D-Var) data assimilation system, and our analyses also focus on the impact of the different elements of the control vector (i.e. the initial conditions, surface forcing, and open boundary conditions) on the circulation. While the influence of each component of the control vector varies between different metrics of the circulation, the impact of each observing system across metrics is very robust. In addition, the mean amplitude of the circulation increments (i.e. the difference between the analysis and background) remains relatively stable throughout the three decade period despite the addition of new observing platforms whose impact is redistributed according to the relative uncertainty of observations from each platform. We also consider the impact of each observing platform on CCS circulation variability associated with low-frequency climate variability. The low-frequency nature of the dominant climate modes in this region allows us to track through time the impact of each observation on the circulation, and illustrates how observations from some platforms can influence the circulation up to a decade into the future.

Development and evaluation of a high-resolution reanalysis of the East Australian Current region using the Regional Ocean Modelling System (ROMS 3.4) and Incremental Strong-Constraint 4-Dimensional Variational (IS4D-Var) data assimilation

Abstract. As with other Western Boundary Currents globally, the East Australian Current (EAC) is highly variable making it a challenge to model and predict. For the EAC region, we combine a high-resolution state-of-the-art numerical ocean model with a variety of traditional and newly available observations using an advanced variational data assimilation scheme. The numerical model is configured using the Regional Ocean Modelling System (ROMS 3.4) and takes boundary forcing from the BlueLink ReANalysis (BRAN3). For the data assimilation, we use an Incremental Strong-Constraint 4-Dimensional Variational (IS4D-Var) scheme, which uses the model dynamics to perturb the initial conditions, atmospheric forcing, and boundary conditions, such that the modelled ocean state better fits and is in balance with the observations. This paper describes the data assimilative model configuration that achieves a significant reduction of the difference between the modelled solution and the observations to give a dynamically consistent “best estimate” of the ocean state over a 2-year period. The reanalysis is shown to represent both assimilated and non-assimilated observations well. It achieves mean spatially averaged root mean squared (rms) residuals with the observations of 7.6 cm for sea surface height (SSH) and 0.4 °C for sea surface temperature (SST) over the assimilation period. The time-mean rms residual for subsurface temperature measured by Argo floats is a maximum of 0.9 °C between water depths of 100 and 300 m and smaller throughout the rest of the water column. Velocities at several offshore and continental shelf moorings are well represented in the reanalysis with complex correlations between 0.8 and 1 for all observations in the upper 500 m. Surface radial velocities from a high-frequency radar array are assimilated and the reanalysis provides surface velocity estimates with complex correlations with observed velocities of 0.8–1 across the radar footprint. A comparison with independent (non-assimilated) shipboard conductivity temperature depth (CTD) cast observations shows a marked improvement in the representation of the subsurface ocean in the reanalysis, with the rms residual in potential density reduced to about half of the residual with the free-running model in the upper eddy-influenced part of the water column. This shows that information is successfully propagated from observed variables to unobserved regions as the assimilation system uses the model dynamics to adjust the model state estimate. This is the first study to generate a reanalysis of the region at such a high resolution, making use of an unprecedented observational data set and using an assimilation method that uses the time-evolving model physics to adjust the model in a dynamically consistent way. As such, the reanalysis potentially represents a marked improvement in our ability to capture important circulation dynamics in the EAC. The reanalysis is being used to study EAC dynamics, observation impact in state-estimation, and as forcing for a variety of downscaling studies.